At the moment the GE will accept any races. However, I believe they have it so that non-human races will not be able to progress into the officer ranks - you'd have to move to one of their nats to progress I think.

Not necessarily, it will depends on your CO what ship you'll pilot and maybe your skills too. And if you'll try hard enough you'll be officer too, not like GE doesn't have any alien officers now. SWC GE is far from Canon, so I wouldn't worry too much about being alien.